Motivated by the inventors' previous application on flexible honeycomb design with negative. Poisson's ratio (NPR) often called ‘auxetic’ [1], more geometric options of hexagonal honeycomb meso-structures are explored including honeycomb having NPR. While designing an effective shear modulus, e.g., G12* of 10 MPa, of hexagonal honeycombs, we are searching honeycomb geometry such as the cell wall thickness, t, the vertical cell length; h, the inclined cell length, l, and the cell angle, θ. Using an aluminum alloy (7075-T6) as the constituent material, the in-plane linear elastic honeycomb model is employed for a numerical parametric study and the honeycomb design. The re-entrant geometry affects the flexible property of NPR honeycombs, resulting in an effective shear yield strength, (T*pl)12 of 1.7 MPa and an effective shear yield strain, (γ*pl)12 of 0.17 when they are designed to have a G12* of 10 MPa.
Hexagonal honeycombs are commonly used cellular materials employed in various applications in the design of light weight structures. For example, the in-plane moduli of hexagonal honeycombs have been successfully investigated with the cell wall bending model, which is called cellular material theory (CMT) [2,3]. There are other analytical and numerical models to describe in-plane effective properties of honeycombs in the literature; a refined cell wall's bending model by adding a beam's stretching and hinging motion [4], a model with the energy method [5], a refined model with round shape at cell edges [6], and a model using the homogenization method [7]. In-plane mechanical properties with different cell types—square, hexagonal, triangle, mixed squares and triangles, diamond—were investigated by Wang and McDowell [8].
Compared to the fundamental studies on cellular solids, their practical applications have been limited to the development of high stiffness-to-weight ratio and high impact energy absorption induced sandwich cores for aircraft and aerospace structures, which are related to the honeycombs' out of plane properties [9-13].
Triangular, Kagome, and diamond cell honeycombs are known to extension dominated cell structures, which is good for a high modulus structural design. On the other hand, square and hexagonal cell honeycombs are known to bending dominated structures, which is good for a flexible structural design [8]. Hexagonal cell structures are known to be flexible in both axial and shear directions [3]. Moreover, hexagonal honeycombs can be easily tailored to have an effective negative Poisson's ratio with negative internal cell angles. This induces the flexible property of the cellular structures due to their re-entrant geometry which is known to increase the buckling loading of honeycombs [4]. Therefore, the hexagonal geometry has a potential to be designed as compliant structures.
Our previous application that focused on tailoring dual target properties, e.g., effective shear modulus and effective shear yield strain, with cellular structures shows a possibility in, building flexible cellular structures [15, 16]. Motivated by our recent findings on the shear compliant hexagonal honeycombs for the shear band component of a lunar rover wheel, we are seeking more geometric and material options for the flexible hexagonal honeycomb design. This study will also be applicable in the aerospace morphing wing technology in which some researchers already began to use the in-plane flexibility with honeycombs [17, 18]. The use of re-entrant cellular structures as micro-actuators and displacement amplifiers has been suggested in the micro-electro-mechanical-system (MEMS) design [19].
The inventors are challenged with developing cellular meso-structures that mimic elastomers' shear properties. In this application, while pursuing an elastomer's shear modulus, 10 MPa, the inventors investigate the effect of various hexagonal geometries on the effective shear strains with an aluminum alloy (7075-T6).